The factorial moments Eq. (REF ), under
the steady state condition, satisfy a hierarchy of relations \(0 =\sum _{k^{\prime }} {\Lambda }_{k k^{\prime }} {\Phi }_{k^{\prime }}\)  By
dividing through by \({\Phi }_k\) , each of these may be written as a
constraint on ratios of neighboring moments \({\Phi }_{k^{\prime }}\)  to
\({\Phi }_k\) . In one dimension (for CRN's involving only one species)
these become recursion relations, which may be solved by a method of
matched asymptotic
expansions [1]}, [2]}
downward from \(k \rightarrow \infty \)  and upward from \(k = 0\) .
